Implement Batch Normalization

medium

Given a two-dimensional tensor (matrix) `data` (where each row represents a sample and each column represents a feature) and epsilon, implement batch normalization without using built-in functions specifically designed for batch normalization. Normalize across the batch (i.e., across rows). Return the normalized data.

Note: By default, torch.var() applies Bessel's correction, using N-1 instead of N as the denominator. The 'Source of Bias' section in the Wikipedia article on Bessel's correction ( https://en.wikipedia.org/wiki/Bessel%27s_correction ) provides a good example to help develop intuition behind this.

X_{norm} = \frac{X - \mu}{\sqrt{\sigma^2 + \epsilon}}

Where:

$X$ : Input data matrix.
$mu$ : Mean of the data across the batch dimension.
$sigma^2$ : Variance of the data across the batch dimension.
$epsilon$ : A small constant added for numerical stability.

Examples:

1.0

0.00001

↓

-1

10.0

0.00001

↓

1.0911

1.0000

-0.8729

0.0000

-0.2182

-1.0000

Implement Batch Normalization

Examples:

Hint

torch.var

torch.mean

torch.sqrt